Story highlights

Trump released Monday a statement calling for U.S. to refuse entry of foreign Muslims

Trump's comments put U.S. national security at risk, Pentagon spokesman said without naming him

Washington (CNN)Donald Trump's statement that Muslims should be banned from entering the United States "disqualifies" him from being president, the White House spokesman said Tuesday.

"The fact is what Donald Trump said yesterday disqualifies him from serving as president," White House press secretary Josh Earnest said in Tuesday's press briefing. For a White House administration to so heavily weigh in on an opposing party's nominating contest is a highly unusual step.

Earnest noted first that every president must take an oath to "preserve, protect and defend" the U.S. Constitution, and thus, he said, Trump would not qualify.

The GOP front-runner on Monday released a statement calling for the U.S. to refuse entry of foreign Muslims. His proposal was met with widespread criticism, including from several candidates in his own party.

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But Earnest had harsh words for the GOP as a whole, too, saying all GOP presidential candidates have signed a pledge to support whoever is the eventual nominee.

"For Republican candidates for president to stand by their pledge to support Mr. Trump, that in and of itself is disqualifying," Earnest said. "The question now is about the rest of the Republican Party and whether or not they're going to be dragged into the dustbin of history with him. And right now the current trajectory is not very good."

Earnest cited the election of House Majority Whip Steve Scalise, who a reporter said once joked he was like white supremacist David Duke "without the baggage," and a leaked Republican Senate campaign memo instructing candidates how to ride voters' support for Trump.

He also noted that House Speaker Paul Ryan Tuesday said he would vote for Trump if he were the GOP nominee -- though he omitted the fact that Ryan unequivocally rebuked Trump's comments and said they were "not who we are as a party" and unconstitutional.

The White House spokesman on Tuesday also called Trump a "carnival barker."

"The Trump campaign for months now has had a dustbin of history-like quality to it," Earnest said.

Comments put U.S. 'at risk'

Secretary of State John Kerry also rebuked Trump's comments.

"I would simply say that nondiscrimination and equal treatment are a pillar of not just American values but of our immigration and our admission policies in this country and the State Department remains totally committed to treating all religions with respect and without discrimination," Kerry said during a press briefing in Paris.

He added, "As I travel around the world, it is clear to me and how both our friends and our adversaries watch and listen to the discourse in the U.S., and I believe that comments such as those that we just heard are not constructive -- and I would say that is putting it diplomatically."

And Pentagon spokesman Peter Cook on Tuesday said -- without hitting the Republican front-runner by name -- that Trump's comments put U.S. national security at risk.

"Anything that bolsters ISIL's narrative and pits the United States against the Muslim faith is certainly not only contrary to our values but contrary to our national security," he said, using another name for ISIS.

He also said that there are "many men and women in uniform today of Muslim faith who are serving this country patriotically."

The U.S. is working with Muslim nations right now, Cook noted. "We want to, in essence, take the fight to ISIL with the help of Muslims around the world."